The change of the Jordan structure under one row perturbations (Q1779388)

\textit{H. den Boer} and \textit{G. Ph. A. Thijsse} [Integral Equations Oper. Theory 3, 23--42 (1980; Zbl 0433.47007)] and \textit{A. S. Markus} and \textit{E. E. Parilis} [Linear Algebra Appl. 54, 139--152 (1983; Zbl 0524.15010)] have solved the problem of describing all the possible Jordan canonical forms of the matrices obtained from a matrix \(M\) by means of a small modification of each of its entries. In the paper under review the authors investigate possible improvements of those results when only a single row of the matrix \(M\) is changed with a small margin of tolerance. Actually, they obtain necessary conditions that have to be satisfied by the similarity invariants of a matrix with one row close enough to that of an assigned matrix. Furthermore, the authors characterize the class of matrices with prescribed invariant factors.